NGC 3603 is the most massive and luminous visible starburst region in the Galaxy. We present the first Chandra/ACIS-I X-ray image and spectra of this dense, exotic object, accompanied by deep cm-wavelength ATCA radio image at similar or less than 1 inch spatial resolution, and HST/ground-based optical data. At the S/N greater than 3 level, Chandra detects several hundred X-ray point sources (compared to the 3 distinct sources seen by ROSAT). At least 40 of these sources are definitely associated with optically identified cluster O and WR type members, but most are not. A diffuse X-ray component is also seen out to approximately 2 feet (4 pc) form the center, probably arising mainly from the large number of merging/colliding hot stellar winds and/or numerous faint cluster sources. The point-source X-ray fluxes generally increase with increasing bolometric brightnesses of the member O/WR stars, but with very large scatter. Some exceptionally bright stellar X-ray sources may be colliding wind binaries. The radio image shows (1) two resolved sources, one definitely non-thermal, in the cluster core near where the X-ray/optically brightest stars with the strongest stellar winds are located, (2) emission from all three known proplyd-like objects (with thermal and non-thermal components, and (3) many thermal sources in the peripheral regions of triggered star-formation. Overall, NGC 3603 appears to be a somewhat younger and hotter, scaled-down version of typical starbursts found in other galaxies.